Leapfrog filter

ABSTRACT

A leapfrog filter comprises a first integrator made up of a first operational amplifier and a first capacitor connected to output terminal of the first operational amplifier; a second integrator made up of a second operational amplifier and a second capacitor connected to inverting input terminal and output terminal of the second operational amplifier; and a variable current source circuit. The first operational amplifier has the output terminal thereof connected to non-inverting input terminal of the second operational amplifier. The second operational amplifier has the output terminal thereof connected to inverting input terminal of the first operational amplifier. An input terminal is connected to non-inverting input terminal of the first operational amplifier; and output terminal connected to the output terminal of the second operational amplifier. The variable current source circuit is arranged such that bias currents supplied to the first and second operational amplifiers are controlled so as to change mutual conductances of the first and first operational amplifiers, thereby adjusting pass band width of the filter while at the same time restraining occurrence of in-band ripple.

BACKGROUND OF THE INVENTION

1. Field of the Invention

This invention relates to leapfrog filter, and more particularly itpertains to such a filter which is so designed as to be easy to adjustthe pass band width thereof and less likely to produce in-band ripple.

2. Description of the Prior Art

Referring to FIG. 1, description will first be made of an example ofconventional active filter, which is constructed in the form of biquadcircuit constituting a low-pass filter. The transfer function T(S) of acommon low-pass filter is given as follows: ##EQU1## where ω₀ is angularfrequency; s is complex variable; Q is quality factor; and H is gainfactor.

The relationship between input and output voltages V₁ and V₂ of thebiquad circuit can be expressed in the form of transfer function T(S) asfollows: ##EQU2##

Assuming that the factor of each term in Equation (1) and that inEquation (2) are equal to each other, the angular frequency ω₀ is givenas follows:

    ω.sub.0.sup.2 =1/R.sub.20 R.sub.40 C.sub.10 C.sub.20

Further, since the angular frequency ω₀ is given as ω₀ =2πF₀, the centerfrequency f₀ can be expressed as follows:

    f.sub.0 =1/2π·√R.sub.20 R.sub.40 C.sub.10 C.sub.20 ( 3)

Still further, from the Equations (1) and (2), the quality factor can beexpressed as follows:

    Q=√R.sub.10.sup.2 C.sub.10 /R.sub.20 R.sub.40 C.sub.20 ( 4)

As will be seen from Equation (3), it is required that circuit constantssuch as resistors R₂₀ and R₄₀ or capacitors C₁₀ and C₂₀ be made variablein an attempt to make variable the center frequency f₀. Thus, to makevariable the center frequency f₀, the conventional biquad circuitrequires externally mounted components such as the resistors R₂₀ and R₄₀or capacitors C₁₀ and C₂₀ which are unsuitable for semiconductorintegrated circuit fabrication. With the conventional biquad circuit, itis required that constants such as resistors R₂₀ and R₂₀ or capacitorsC₁₀ and C₂₀ be changed when it is attempted to provide the desiredcenter frequency f₀. As will be noted from Equation (4), however, thequality factor Q is also changed by adjusting the externally mountedcomponents, and this requires that the other circuit constants be alsochanged.

Furthermore, the conventional active filter such as shown in FIG. 1 isdisadvantageous in that the manufacturing cost is high because a numberof electronic components are mounted onto a printed circuit board.Another disadvantage is such that when it is attempted to adjust thecenter frequency f₀ of the filter, it is required that such adjustmentbe effected with components having the circuit constants thereof set atpredetermined values being mounted on the printed circuit board, andthis inevitably increases the number of steps for band-width adjustmentand assembling of the filter.

SUMMARY OF THE INVENTION

The present invention has been made with a view to obviating theaforementioned drawbacks of the prior art. Accordingly, it is a primaryobject of the present invention to provide a leapfrog filter which is sodesigned to be easier to adjust the center frequency f₀ and set up thepass band width.

Another object of the present invention is to provide a leapfrog filterwhich is designed so that in-band ripple is less likely to occur whenadjustment of the pass band width is effected.

Still another object of the present invention is to provide a leapfrogfilter which is so designed as to have the number of components reducedand to be well adapted for fabrication in the form of semiconductorintegrated circuit.

Briefly stated, according to an aspect of the present invention, thereis provided a leapfrog filter which comprises a first integrator made upof a first operational amplifier and a capacitor connected to outputterminal of the first operational amplifier; a second integrator made upof a second operational amplifier and a second capacitor connected toinverting input terminal and output terminal of the second operationalamplifier; and a variable current source circuit. The first operationalamplifier has the output terminal thereof connected to non-invertinginput terminal of the second operational amplifier. The secondoperational amplifier has the output terminal thereof connected toinverting input terminal of the first operational amplifier. An inputterminal is connected to non-inverting input terminal of the firstoperational amplifier; and output terminal connected to the outputterminal of the second operational amplifier. The variable currentsource circuit is arranged such that bias currents supplied to the firstand second operational amplifiers are controlled so as to change mutualconductances of the first and first operational amplifiers, therebyadjusting pass band width of the filter while the same time restrainingoccurrence of in-band ripple.

Other objects, features and advantages of the present invention willbecome apparent from the ensuing description taken in conjunction withthe accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a circuit diagram showing a biquad circuit constituting anexample of conventional active filter.

FIG. 2 is a circuit diagram showing the leapfrog filter according to anembodiment of the present invention.

FIG. 3 is a circuit diagram showing the leapfrog filter according toanother embodiment of the present invention.

FIG. 4 illustrates the frequency characteristics of the embodiment shownin FIG. 2.

FIG. 5 illustrates the frequency characteristics of the embodiment shownin FIG. 3.

FIG. 6 is a circuit diagram showing a more practical version of thearrangement of FIG. 3.

FIG. 7 shows an equivalent circuit of a secondary low-pass filter.

FIG. 8 is a feedback diagram of the secondary low-pass filter.

FIG. 9 illustrates the relationship between a variable current i_(W) andcurrent i₁, i₂.

DESCRIPTION OF THE PREFERRED EMBODIMENTS

Referring to FIG. 2 of the accompanying drawings, there is shown theleapfrog filter according to an embodiment, wherein an input terminal 1is connected to non-inverting terminal of an operational amplifier A₁,the output terminal of which is coupled to a capacitor C₁, and also tonon-inverting terminal of another operational amplifier A₂. Invertingterminal of the operational amplifier A₁ is connected to the outputterminal and inverting terminal of the operational amplifier A₂, andalso to a capacitor C₂ and an output terminal 2. The operationalamplifier A₁, together with the capacitor C₁ connected to the outputterminal thereof, constitutes an integrator 3; and the operationalamplifier A₂ also, together with the capacitor C₂ coupled to the outputterminal thereof, constitutes an integrator 4. The integrator 4 is of aself negative feedback type wherein the inverting input terminal of theoperational amplifier A₂ is connected to the output terminal thereof.The integrator 3 has its output terminal coupled to the non-invertinginput terminal of the operational amplifier A₂, the output terminal ofwhich in turn is connected to the inverting input terminal of theoperational amplifier A₁, so that negative feedback is applied thereto.In this way, a secondary low-pass filter is formed.

A variable current source circuit 7 is arranged to supply currents i₁and i₂ to the operational amplifiers A₁ and A₂ as bias currentsrespectively through current source circuits 5 and 6 each of whichcomprises a current-mirror circuit. The variable current source circuit7 comprises transistors Q₁ and Q₂ which are biased with forward voltageof a diode D₁, to which a current i_(W) is supplied from a variablecurrent source circuit I₁ ; and the current source circuits 5 and 6connected to the collectors of the transistors Q₁ and Q₂ respectively.The current source circuit 5 comprises a current-mirror circuit which isconstituted by a diode D₂ and transistor Q₉, and the current sourcecircuit 6 also comprises a current-mirror circuit which is formed by adiode D₃ and transistor Q₁₀.

With such a leapfrog filter, collector currents i₁ and i₂ of thetransistors Q₁ and Q₂ are drawn in through the current source circuits 5and 6 so that the currents i₁ and i₂, i.e., mirror currentscorresponding to variations in the variable current i_(w) are suppliedfrom the transistors Q₉ and Q₁₀ provided at the output stage of thecurrent source circuits 5 and 6 to the operational amplifiers A₁ and A₂respectively. The relationship between the variable current i_(W) andthe currents i₁, i₂ is shown at (a) in FIG. 9.

The filter characteristics of the embodiment shown in FIG. 2, areillustrated in FIG. 4, wherein the abscissa indicates frequency, and theordinate represents attenuation. As the variable current i_(W) isincreased, the currents i₁ and i₂ supplied to the operational amplifiersA₁ and A₂ through the current source circuits 5 and 6 respectively arealso increased. In such a case, the frequency characteristics of thefilter is changed as indicated at (a), (b) and (c) in FIG. 4, from whichit will be noted that the center frequency f₀ is changed toward highervalues f₀₁, f₀₂ so that the pass band width is increased.Disadvantageously, however, as the variable current i_(W) is increased,the quality factor Q will also be changed due to element sensitivityvariations which tend to result from deterioration in the high-frequencycharacteristics of elements constituting the leapfrog filter. Suchvariations in the in-band characteristic of the filter will increasein-band ripple such as shown in FIG. 4. For the case where flatfrequency characteristic is required, such a problem of in-band ripplecan be most effectively coped with by means of such an arrangement asshown in FIG. 3.

FIG. 3 shows the leapfrog filter according to a second embodiment of thepresent invention, which is different from the embodiment of FIG. 2 inrespect of variable current source circuit 7. In this embodiment, thevariable current source circuit 7 includes transistors Q₁ , Q₂ and Q₃each having its base connected to the anode of a diode D₁ to which acurrent i_(W) is supplied from a variable current source I₁. Thetransistor Q₁ has its collector connected to the emitter of a transistorQ₄ which has its collector coupled to the cathode of a diode D₂ and tothe base of a transistor Q₉. The current i₁ is supplied to theoperational amplifier A₁ through the transistor Q₉. The collector of thetransistor Q₂ is connected to the emitter of the transistor Q₅, and thecollector of the transistor Q₅ is coupled to the cathode of a diode D₃,and to base of the transistor Q₁₀. The current i₂ is supplied to theoperational amplifier A₂ through the transistor Q₁₀. Further, a resistorR₁ is connected between the collectors of the transistors Q₁ and Q₂. Thecollector of the transistor Q₃ is connected to the base of thetransistor Q₄, the collector of transistor Q₆, and one end of a resistorR₃. Transistors Q₆ to Q₈ have their bases coupled to the cathode of adiode D₈, and to a constant current source circuit I₂. A resistor R₅ isconnected at one end to the emitter of the transistor Q₈, the other endof the resistor R₅ being coupled to a voltage source B. The collector ofthe transistor Q₈ is connected to the emitter of the transistor Q₃ andresistor R₂. The collector of the transistor Q₇ is connected to the baseof the transistor Q₅ and resistor R₄. The resistors R₂ to R₄ aregrounded at the other ends. As in the embodiment shown in FIG. 2, thecurrent source circuit 5 comprises a current mirror circuit constitutedby the diode D₂ and transistor Q₉, and the current source circuit 6comprises a current mirror circuit formed by the diode D₃ and transistorQ₁₀. Currents i₁ and i₂ are supplied to the operational amplifiers A₁and A₂ through these current source circuits 5 and 6 so that the mutualconductance of each of these operational amplifiers A₁ and A₂ isadjusted.

With the embodiment of FIG. 3, variable current i_(W) derived from thevariable current source circuit I₁ is supplied to the diode D₁ so thatthe transistors Q₁ to Q₃ are biased. Meanwhile, constant current i₀ isbeing drawn in by the constant current source circuit from the diode D₈and transistors Q₆ to Q₈, so that the transistors Q₆ to Q₈ are biasedwith the forward voltage of the diode D₈. Current i₀ ' is supplied tothe resistor R₂ through the transistor Q₈, and the voltage across theresistor R₂ and the forward voltage of the diode D₁ are compared witheach other by means of the transistor Q₃. If the forward voltage of thediode D₁ is lower than the voltage across the resistor R₂, then thetransistor Q₃ is turned off so that current i₀ is supplied to resistorsR₃ and R₄ through the transistors Q₆ and Q₇ respectively so that thetransistor Q₄ and Q₅ are biased with equal terminal voltages occurringacross the resistors R₃ and R₄ respectively; and collector currents i₁and i₂ are drawn in from the current source circuits 5 and 6 so that theequal currents i₁ and i₂ are supplied to the operational amplifiers A₁and A₂ through the transistors Q₉ and Q₁₀ at the output stages of thecurrent source circuits 5 and 6 respectively.

By increasing the current I_(W) provided by the variable current sourcecircuit I₁, the forward voltage of the diode D₁ is caused to build up;and when the forward voltage becomes higher than the terminal voltage ofthe resistor R₂, the transistor Q₃ is rendered operative so thatcollector current i_(C3) is caused to flow. At the same time, collectorcurrents i_(C1) and i_(C2) of the transistors Q₁ and Q₂ are alsoincreased. Current i₀ supplied from the transistor Q₆ to the resister R₃is lower by the amount of the collector current i_(C3) than current i₀supplied from the transistor Q₇ to the resistor R₄ ; thus, base currenti_(B1) of the transistor Q₄ is decreased. For the increase in thevariable current i_(W), currents i₁ and i₂ depending on base currentsi_(B1) and i_(B2) of the transistors Q₄ and Q₅ are supplied to theoperational amplifiers A₁ and A₂ through the current source circuits 5and 6 respectively.

Referring to FIG. 9, there is illustrated the relationship between thevariable current i_(w) and the currents i₁, i₂, wherein the abscissaindicates the value of the variable current i_(W), and the ordinaterepresents the values of the bias currents i₁, i₂. In FIG. 9, theoperational characteristic of the embodiment shown in FIG. 3 is shown at(a). From FIG. 9, it will be noted that the variable current sourcecircuit 7 provided in the embodiment of FIG. 3, the current i₁ suppliedto the operational amplifier A₁ is controlled so that its increasingrate is restrained with respect to the current i₂ supplied to theoperational amplifier A₂. Thus, it is possible to change the centerfrequency f₀ by controlling the currents i₁, i₂ with respect tovariations in the variable current i_(w). In this way, the filtercharacteristic of this embodiment can be made to be such a flat one asshown in FIG. 5 wherein by increasing the current i_(w), the centerfrequency f₀ is changed to a higher frequency such as f₀₁, f₀₂ so thatthe pass band width is expanded and occurrence of ripple is restrained.

FIG. 6 illustrates a more practical version of the leapfrog filteraccording to the embodiment shown in FIG. 2. In FIG. 6, an operationalamplifier A₁ comprises a differential pair of transistors Q₁₂ and Q₁₃having their collectors connected to the collectors of transistors Q₁₄and Q₁₅ which constitute a current-mirror circuit. The emitters of thetransistors Q₁₂ and Q₁₃, which are connected together, are connected tothe collector of a transistor Q₁₁, the emitter of which is coupled to apower source voltage B. The transistors Q₁₂ and Q₁₃ have their basesconnected to the cathodes of diodes D₄ and D₅, the anodes of which areconnected together and to a current source comprising a diode or thelike. Further, the bases of the transistors Q₁₂ and Q₁₃ are coupled tothe collectors of transistors Q₁₆ and Q₁₇ respectively; a resistor R₁₀is connected between the emitters of the transistors Q₁₆ and Q₁₇ ; andthe emitters of the transistors Q.sub. 16 and Q₁₇ are grounded throughthe current source. A capacitor C₁ is connected to the inter-connectedcollectors of the transistors Q₁₂ and Q₁₄ ; and the operationalamplifier A₁, together with the capacitor C1, constitutes an integratingcircuit 3 which in turn is connected to the base of a transistor Q₂₃provided in a succeeding operational amplifier A₂. The transistor Q₁₁ isconnected with diode D₂ so as to constitute a current-mirror circuit,and the connection is made such that the current i₁ is supplied to theoperational amplifier A₁.

The operational amplifier A₂ comprises Q₁₉ and Q₂₀ having theircollectors connected to the collectors of transistors Q₂₁ and Q₂₂respectively, the transistors Q₂₁ and Q₂₂ constituting a current-mirrorcircuit. The inter-connected emitters of the transistors Q₁₉ and Q₂₀ areconnected to the collector of transistor Q₁₈, the emitter of which iscoupled to the power source voltage B. The transistors Q₁₉ and Q₂₀ havetheir bases connected to the cathodes of diodes D₆ and D₇ respectively,the anodes of the diodes D₆ and D₇ being connected together and to acurrent source comprising a diode or the like. A resistor R₁₁ isconnected between the emitters of transistors Q₂₃ and Q₂₄, the emittersof which are grounded through current sources respectively. Thetransistor Q₂₃ has its base connected to capacitor C₁. Capacitor C₂ iscoupled to the inter-connected collectors of the transistors Q₁₉ and Q₂₁and to the base of the transistor Q₁₇ of the integrating circuit 3, thecapacitor C₂ being also connected to the output terminal 2. TransistorQ₁₈ is connected with diode D₃ so as to constitute a current-mirrorcircuit, and the connection is made such that the current i₂ is suppliedto the operational amplifier A₁. Variable current source circuit 7 isidentical with that provided in the embodiment of FIG. 2, and thereforedescription of the construction thereof will be omitted.

Description will now be made of the operation of the integrating circuitof the leapfrog filter shown in FIG. 6, wherein V_(i) indicates inputvoltage; V_(o) represents output voltage; and I₁ and I_(x) denote biascurrent. Let it be assumed that signal component current is i_(o) ; thatcurrent flowing through the resistor R₁₀ is i_(a) ; and that AC voltageV_(i) applied to the bases of the transistors Q₁₂ and Q₁₅. Then, thefollowing equation holds:

ti i_(a) =V_(i) /R₁₀ (5)

Also let it be assumed that the difference between the base voltages ofthe transistors Q₁₂ and Q₁₃ is V_(a). The following relationship holdstrue: ##EQU3## where I_(s1) and I_(s2) are saturation currents betweenthe base and emitter of the transistors Q₁₂ and Q₁₃ which are equal toeach other; and V_(T) is thermal voltage.

The following equations are derived from Equations (6) and (7):

    ln(I.sub.1 +i.sub.a)/(I.sub.1 -i.sub.a)=ln(I.sub.x +i.sub.a)/(I.sub.x -i.sub.a)

    (I.sub.1 +i.sub.a)/(I.sub.1 -i.sub.a)=(I.sub.x +1.sub.a)/(I.sub.x -i.sub.a)

By rearranging the above expressions and putting Equation (5) therein,the signal current i_(o) is given as follows:

    i.sub.o =I.sub.x i.sub.a /I.sub.1 =I.sub.x ΔV.sub.1 /I.sub.1 R.sub.10 (8)

Output voltage V_(o) of the integrating circuit is given

    V.sub.o =I.sub.x V.sub.i /I.sub.1 R.sub.10 sC              (9)

Thus, the following equation is derived from Equation (9):

    V.sub.o /V.sub.i =I.sub.x /I.sub.1 ·1/R.sub.10 ·1/sC (10)

From Equation (9), mutual conductance gm may be expressed as follows:

    gm=∂i.sub.o /∂V.sub.o =I.sub.x /I.sub.1 ·1/R.sub.10                                      (11)

Then, the transfer function T(S) of the integrating circuit shown inFIG. 5 can be written as follows:

    T(S)=V.sub.o /V.sub.i =gm/sC=1/srC

where r=1/gm.

It is apparent that the mutual conductance of the operational amplifierA₁ is such that r=1/gm, and that the transfer function T(S) of theintegrator depends on the function of bias current I₁, I_(x) andresistance R₁₀. It will be seen that the integrating circuit changes thetransfer function T(S) of the integrator by controlling the bias currentI_(x).

Description will now be made of the secondary leapfrog filter shown inFIG. 2 using the above-mentioned integrating circuit, by referring tothe equivalent circuit of the secondary leapfrog filter shown in FIG. 6.

Based on the equivalent circuit of FIG. 6, the following equations hold:

    I.sub.1 =Y.sub.1 (V.sub.1 -V.sub.2)                        (12)

    V.sub.2 =Z.sub.2 ·I.sub.1                         (13)

By using voltage quantities, these two equations can be rewritten asfollows:

    V I.sub.1 =T.sub.y1 (V.sub.1 -V.sub.2)                     (14)

    V.sub.2 =T.sub.z2 ·V.sub.11                       (15)

The following equations are also obtained:

    T.sub.y1 =1/s L where s=jω

    T.sub.z2 =1/(1+s C)

From such expressions, it is possible to depict the signal diagram shownin FIG. 7.

The admittance Y1 of coil L shown in the equivalent circuit diagram ofFIG. 6 is given as follows: ##EQU4## Since gm=1/r, Equation (16) can berewritten as follows:

    A(s)=1/s L r

By letting r=1, Equation (16) is rewritten as follows:

    A(s)=1/s L                                                 (17)

The impedance Z₂ of the equivalent circuit of FIG. 6 is expressed interms of transfer function B(s) as follows: ##EQU5##

By letting r=1, Equation (18) is rewritten as follows:

    B(s)=1/(1+s C)

Thus, the total transfer function T¢(s) of the leapfrog filter is givenas follows: ##EQU6##

A(s) and B(s) can be rewritten as follows: ##EQU7## The transferfunctions A(s) and B(s) can also be rewritten as follows:

    A(s)=1/sL=Q ω.sub.o /s                               (22)

By letting 1/s C=ω_(o) /s Q, the transfer function B(s) of Z₂ is writtenas below. ##EQU8##

Thus, by putting Equations (22) and (23) in Equation (19) it is possibleto express the total transfer function T(s) as follows: ##EQU9##

Description will next be made of the variable current source circuit 7of the leapfrog filter shown in FIG. 2.

Let it be assumed that r (r=1/gm) of the operational amplifiers 3 and 5constituting the integrators is r₁ and r₂ respectively, and that thecapacitance of the capacitors 4 and 6 is C₁ and C₂ respectively. Thetransfer function of each integrator is then expressed as follows:

    Q ω.sub.o /s=1/s r.sub.1 C.sub.1

    ω.sub.o /s Q=1/s r.sub.2 C.sub.2

Further, by rearranging the above equations, the following expressionscan be obtained:

    Q ω.sub.o =1/s r.sub.1 C.sub.1                       (25)

    ω.sub.o /Q=1/r.sub.2 C.sub.2                         (26)

Still further, the following equations hold true:

    1/r.sub.1 =gm.sub.1 =i.sub.1 /I.sub.1 ·R.sub.10

    1/r.sub.2 =gm.sub.2 =i.sub.2 /I.sub.2 ·R.sub.10

By rearranging the above expressions, it is possible to obtain thefollowing equations:

    r.sub.1 =I.sub.1 ·R.sub.10 /i.sub.1               (27)

    r.sub.2 =I.sub.1 ·R.sub.10 /i.sub.2               (28)

Thus, the quality factor Q can be sought from Equations (25) and (26) asmentioned below. By putting Equations (27) and (28) in the expressionthus sought, the following equations are obtained: ##EQU10##Consequently, the quality factor Q can be written as follows:

    Q=(C.sub.2 i.sub.1 /C.sub.1 i.sub.2).sup.1/2               (29)

The center frequency ω_(o) is sought from Equations (27) and (28). Byputting Equations (27) and (28) in the resultant expression, thefollowing expression is obtained: ##EQU11## Consequently, the centerfrequency ω_(o) is expressed as follows:

    ω.sub.o =1/I.sub.1 R.sub.10 ·(i.sub.1 i.sub.2 /C.sub.1 C.sub.2).sup.1/2                                          (30)

Let it be assumed that the factor C₂ /C₁ in Equation (29) is C_(K) whichis constant, and that the factor 1/I₁ R₁₀ (C₁ C₂)^(1/2) is C₁ which isalso constant. The quality factor Q is given as follows: ##EQU12##

As will be seen from Equations (31) and (32), the relationship betweenthe currents i₁ and i₂ is that of multiplication and division. Further,by making different the bias currents i₁ and i₂ supplied to theoperational amplifiers A₁ and A₂ in terms of increasing rate as shown inFIG. 9, the filter characteristic can automatically be made to be flateven though the center frequency is changed as shown at (a), (b) and (c)in FIG. 5. More specifically, by making the increasing rate of thecurrent i₁ supplied to the operational amplifier A₁ at the signal inputstage lower than the increasing rate of the current i₂ supplied to theoperational amplifier A₂, it is possible to restrain the quality factorQ from being increased with an increase in the center frequency f₀ insuch a manner that the quality factor Q turns out to be substantiallyuniform. In this way, it is possible to prevent in-band ripple frombeing increased due to variations in the in-band filter characteristicas shown in the frequency characteristics of FIG. 4, thereby achievingsuch a flat frequency response as shown in FIG. 5.

While in the foregoing embodiment, description has been made of the caseof secondary low-pass filter, it is to be understood that even for anN-th order low-pass filter, it is possible to achieve the same result bycontrolling currents flowing in integrating circuits at the input andoutput stages on the basis of similar concept.

As will be appreciated from the above discussion, the present inventionprovides a leapfrog filter comprising an active filter which is welladapted for fabrication in the form of semiconductor integrated circuitand in which the number of externally mounted components is reduced ascompared with the conventional one; and the in-band pass band width ofthe filter can be varied by increasing or decreasing the sum of currentsi₁ and i₂ supplied to integrators constituting the present leapfrogfilter. A further advantage is such that occurrence of in-band ripplecan be restrained by changing the increasing rates of the currents i₁and i₂.

As discussed above, the present leapfrog filter can be formed by anactive filter in the form of a semiconductor integrated circuit so thatthe number of externally mounted components can be reduced; thus,according to the present invention, there is provided an expensive,miniaturized active filter.

While the present invention has been illustrated and described withrespect to specific embodiments thereof, it is to be understood that thepresent invention is by no means limited thereto but encompasses allchanges and modifications which will become possible within the scope ofthe appended claims.

We claim:
 1. A leapfrog filter comprising:a first integrator made up ofa first operational amplifier and a first capacitor connected to anoutput terminal of said first operational amplifier; a second integratormade up of a second operational amplifier of a self negative feedbacktype and a second capacitor connected to an inverting input terminal andoutput terminal of said second operational amplifier; said firstoperational amplifier having the output terminal thereof connected to anon-inverting input terminal of said second operational amplifier; saidsecond operational amplifier having the output terminal thereofconnected to an inverting input terminal of said first operationalamplifier; an input terminal connected to a non-inverting input terminalof said first operational amplifier; an output terminal connected to theinverting input terminal of said first operational amplifier and theoutput terminal of said second operational amplifier; a variable currentsource circuit including a first and a second current source circuit forfeeding bias currents of different increasing rates to said first andsecond operational amplifiers in such a manner that the increasing rateof the current supplied to the first operational amplifier is restrainedwith respect to the increasing rate of the current supplied to thesecond operational amplifier thereby restraining occurrence of in-bandripple so as to change pass band width of said filter.